Effective field theory for dilute Fermi systems at fourth order

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or kFas expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well converged at this order for |kFas|≲0.5. Furthermore, we show that Padé-Borel resummations can improve the convergence for |kFas|≲1. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter

Constrained extrapolation problem and order-dependent mappings

We consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. We find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties

Neutron matter at finite temperature based on chiral effective field theory interactions

We study the equation of state of neutron matter at finite temperature based on two- and three-nucleon interactions derived within chiral effective field theory to next-to-next-to-next-to-leading order. The free energy, pressure, entropy, and internal energy are calculated using many-body perturbation theory including terms up to third order around the self-consistent Hartree-Fock solution. We include contributions from three-nucleon interactions without employing the normal-ordering approximation and provide theoretical uncertainty estimates based on an order-by-order analysis in the chiral expansion. Our results demonstrate that thermal effects can be captured remarkably well via a thermal index and a density-dependent effective mass. The presented framework provides the basis for studying the dense matter equation of state at general temperatures and proton fractions relevant for core-collapse supernovae and neutron star mergers

New equations of state constrained by nuclear physics, observations, and QCD calculations of high-density nuclear matter

We present new equations of state for applications in core-collapse supernova and neutron star merger simulations. We start by introducing an effective mass parametrization that is fit to recent microscopic calculations up to twice saturation density. This is important to capture the predicted thermal effects, which have been shown to determine the proto-neutron star contraction in supernova simulations. The parameter range of the energy-density functional underlying the equation of state is constrained by chiral effective field theory results at nuclear densities as well as by functional renormalization group computations at high densities based on QCD. We further implement observational constraints from measurements of heavy neutron stars, the gravitational wave signal of GW170817, and from the recent NICER results. Finally, we study the resulting allowed ranges for the equation of state and for properties of neutron stars, including the predicted ranges for the neutron star radius and maximum mass.Comment: 21 pages, 19 figures, minor changes, published versio

The physics of dynamical atomic charges: the case of ABO3 compounds

Based on recent first-principles computations in perovskite compounds, especially BaTiO3, we examine the significance of the Born effective charge concept and contrast it with other atomic charge definitions, either static (Mulliken, Bader...) or dynamical (Callen, Szigeti...). It is shown that static and dynamical charges are not driven by the same underlying parameters. A unified treatment of dynamical charges in periodic solids and large clusters is proposed. The origin of the difference between static and dynamical charges is discussed in terms of local polarizability and delocalized transfers of charge: local models succeed in reproducing anomalous effective charges thanks to large atomic polarizabilities but, in ABO3 compounds, ab initio calculations favor the physical picture based upon transfer of charges. Various results concerning barium and strontium titanates are presented. The origin of anomalous Born effective charges is discussed thanks to a band-by-band decomposition which allows to identify the displacement of the Wannier center of separated bands induced by an atomic displacement. The sensitivity of the Born effective charges to microscopic and macroscopic strains is examined. Finally, we estimate the spontaneous polarization in the four phases of barium titanate.Comment: 25 pages, 6 Figures, 10 Tables, LaTe

Phonons and related properties of extended systems from density-functional perturbation theory

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudo-potential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long wave-length vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.Comment: 52 pages, 14 figures, submitted to Review of Modern Physic

Dilute Fermi gas at fourth order in effective field theory

Using effective field theory methods, we calculate for the first time the complete fourth-order term in the Fermi-momentum or $k_{\rm F} a_s$ expansion for the ground-state energy of a dilute Fermi gas. The convergence behavior of the expansion is examined for the case of spin one-half fermions and compared against quantum Monte-Carlo results, showing that the Fermi-momentum expansion is well-converged at this order for $| k_{\rm F} a_s | \lesssim 0.5$.Comment: 6 pages, 2 figures; v2: minor improvements in text, references updated, matches published versio

Effective field theory for dilute Fermi systems at fourth order

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or $k_{\rm F} a_s$ expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well-converged at this order for ${| k_{\rm F} a_s | \lesssim 0.5}$. Further, we show that Pad{\'e}-Borel resummations can improve the convergence for ${| k_{\rm F} a_s | \lesssim 1}$. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.Comment: 18 pages, 5 figures, minor changes, published versio

Chiral Effective Field Theory and the High-Density Nuclear Equation of State

Born in the aftermath of core-collapse supernovae, neutron stars contain matter under extraordinary conditions of density and temperature that are difficult to reproduce in the laboratory. In recent years, neutron star observations have begun to yield novel insights into the nature of strongly interacting matter in the high-density regime where current theoretical models are challenged. At the same time, chiral effective field theory has developed into a powerful framework to study nuclear matter properties with quantified uncertainties in the moderate-density regime for modeling neutron stars. In this article, we review recent developments in chiral effective field theory and focus on many-body perturbation theory as a computationally efficient tool for calculating the properties of hot and dense nuclear matter. We also demonstrate how effective field theory enables statistically meaningful comparisons among nuclear theory predictions, nuclear experiments, and observational constraints on the nuclear equation of state